We present a theoretical framework for describing the integer quantum Hall effect (IQHE) in three-dimensional (3D) electron systems. This work extends our previous single-electron approach, originally applied to two-dimensional (2D) systems such as quantum wells and graphene. Starting from the graphene model—where the unconventional Hall plateau sequence \(2(2n+1)\) arises from Landau quantization—we generalize the formulation to 3D semimetals with low carrier density and high mobility. Using the Poisson summation method, we derive the density of states in a magnetic field, incorporating Gaussian Landau-level broadening, spin splitting, and thermal damping. The model captures both Shubnikov–de Haas oscillations and quantized Hall conductivities. The resulting Hall conductivity shows quantized values proportional to \(2e^2/(h\lambda _F)\) , consistent with experimental reports of 3D quantum Hall states. These results offer a unified description of quantum magnetotransport across dimensions and identify key parameters governing the IQHE in 3D semimetals.
